Chemical Kinetics Section 7 PDF

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This document provides an overview of chemical kinetics, including reaction rates, factors affecting reaction rates, reaction mechanisms, integrated rate laws, and various concepts like the Arrhenius equation. It covers topics from a fundamental perspective as well as advanced concepts.

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Chemical Kinetics Section 7 1 Kinetics Studies the rate at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs)....

Chemical Kinetics Section 7 1 Kinetics Studies the rate at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs). 2 Outline: Kinetics Reaction Rates How we measure rates. How the rate depends on amounts Rate Laws of reactants. How to calc amount left or time to Integrated Rate Laws reach a given amount. How long it takes to react 50% of Half-life reactants. Arrhenius Equation How rate constant changes with T. Link between rate and molecular Mechanisms scale processes. 3 Factors That Affect Reaction Rates 1. Concentration of Reactants As the concentration of reactants increases, so does the likelihood that reactant molecules will collide. 2. Physical state When the reactants are in the same phase, as in an aqueous solution, increased random thermal motion 3. Temperature At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. 4. Catalysts Speed reaction by changing mechanism. 4 5 Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time. [A] vs t 6 Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times, t. 7 Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) The average rate of the reaction over each interval is the change in concentration divided by the change in time: 8 Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Note that the average rate decreases as the reaction proceeds. This is because as the reaction goes forward, there are fewer collisions between reactant molecules. 9 Reaction Rates 10 Reaction Rates 1. Average rate: Over a given period of time, the average rate is the slope of the line joining two points along the curve. 2. Instantaneous rate: The rate at a particular instant during the reaction. The slope of a line tangent to the curve at any point gives instantaneous rate at that time. 3. Initial rate: the instantaneous rate at the moment the reactants are mixed is the initial rate (at t=0) 11 Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) A plot of concentration vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. 12 Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) The reaction slows down with time because the concentration of the reactants decreases. 13 Reaction Rates and Stoichiometry C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1. Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH. -[C4H9Cl] [C4H9OH] Rate = = t t 14 Reaction Rates and Stoichiometry What if the ratio is not 1:1? H2(g) + I2(g) 2 HI(g) Only 1/2 HI is made for each H2 used. 15 Reaction Rates and Stoichiometry To generalize, for the reaction aA + bB cC + dD Reactants (decrease) Products (increase) 16 Concentration and Rate Each reaction has its own equation that gives its rate as a function of reactant concentrations. this is called its Rate Law To determine the rate law, we measure the rate at different starting concentrations. 17 Concentration and Rate Compare Experiments 1 and 2: when [NH4+] doubles, the initial rate doubles. 18 Concentration and Rate Likewise, compare Experiments 5 and 6: when [NO2-] doubles, the initial rate doubles. 19 Concentration and Rate This equation is called the rate law, and k is the rate constant 20 Rate Laws A rate law shows the relationship between the reaction rate and the concentrations of reactants. k is a constant that has a specific value for each reaction. The value of k is determined experimentally. “Constant” is relative here- k is unique for each reaction k changes with T 21 Rate Laws Exponents tell the order of the reaction with respect to each reactant. This reaction is First-order in [NH4+] First-order in [NO2−] The overall reaction order can be found by adding the exponents on the reactants in the rate law. This reaction is second-order overall. 22 Rate Laws For a general reaction occurring at a fixed temperature, aA + bB cC + dD The Rate Law is, Rate = k [A]m[B]n The balancing coefficients a and b in the reaction equation are not necessarily related in any way to the reaction orders m and n The components of the rate law- rate, reaction orders, and rate constants must be found by experiments 23 Integrated Rate Laws Consider a simple 1st order rxn: A B Differential form: How much A is left after time t? Integrate: 24 Integrated Rate Laws The integrated form of first order rate law: Can be rearranged to give: [A]0 is the initial concentration of A (t=0). [A]t is the concentration of A at some time, t, during the course of the reaction. 25 Integrated Rate Laws Manipulating this equation produces… …which is in the form y = mx + b 26 First-Order Processes If a reaction is first-order, a plot of ln [A]t vs. t will yield a straight line with a slope of -k. So, use graphs to determine reaction order. 27 First-Order Processes Consider the process in which methyl isonitrile is converted to acetonitrile. CH3NC CH3CN How do we know this is a first order rn? 28 First-Order Processes CH3NC CH3CN This data was collected for this reaction at 198.9°C. Does rate=k[CH3NC] for all time intervals? 29 First-Order Processes When ln P is plotted as a function of time, a straight line results. The process is first-order. k is the negative slope: 5.1  10-5 s-1. 30 Second-Order Processes Similarly, integrating the rate law for a process that is second-order in reactant A: Rearrange, integrate: also in the form y = mx + b 31 Second-Order Processes So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line with a slope of k. First order: If a reaction is first-order, a plot of ln [A]t vs. t will yield a straight line with a slope of -k. 32 Determining reaction order The decomposition of NO2 at 300°C is described by the equation NO2 (g) NO (g) + 1/2 O2 (g) and yields these data: Time (s) [NO2], M 0.0 0.01000 50.0 0.00787 100.0 0.00649 200.0 0.00481 300.0 0.00380 33 Determining reaction order Graphing ln [NO2] vs. t yields: The plot is not a straight line, so the process is not first-order in [A]. Time (s) [NO2], M ln [NO2] 0.0 0.01000 -4.610 50.0 0.00787 -4.845 Does not fit: 100.0 0.00649 -5.038 200.0 0.00481 -5.337 300.0 0.00380 -5.573 34 Second-Order Processes A graph of 1/[NO2] vs. t gives this plot. Time (s) [NO2], M 1/[NO2] This is a straight 0.0 0.01000 100 line. Therefore, the process is 50.0 0.00787 127 second-order in 100.0 0.00649 154 [NO2]. 200.0 0.00481 208 300.0 0.00380 263 35 Half-Life Half-life is defined as the time required for one-half of a reactant to react. Because [A] at t1/2 is one-half of the original [A], [A]t = 0.5 [A]0. 36 Half-Life For a first-order process, set [A]t=0.5 [A]0 in integrated rate equation: NOTE: For a first-order process, the half-life does not depend on [A]0. 37 Half-Life- 2nd order For a second-order process, set [A]t=0.5 [A]0 in 2nd order equation. 38 Outline: Kinetics 39 The Collision Model In a chemical reaction, bonds are broken and new bonds are formed. Molecules can only react if they collide with each other. 40 The Collision Model Furthermore, molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation. 41 The Collision Theory The collision theory explains why we multiply the concentrations in the rate law to obtain the observed rate law. 42 Activation Energy In other words, there is a minimum amount of energy required for reaction: the activation energy, Ea. Just as a ball cannot get over a hill if it does not roll up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation energy barrier. 43 Reaction Coordinate Diagrams It is helpful to visualize energy changes throughout a process on a reaction coordinate diagram like this one for the rearrangement of methyl isonitrile. 44 Reaction Coordinate Diagrams It shows the energy of the reactants and products (and, therefore, E). The high point on the diagram is the transition state. The species present at the transition state is called the activated complex. The energy gap between the reactants and the activated complex is the activation energy barrier. 45 Temperature and Rate Generally, as temperature increases, so does the reaction rate. This is because k is temperature dependent. 50 Arrhenius Equation Svante Arrhenius developed a mathematical relationship between k and Ea: where A is the frequency factor, a number that represents the likelihood that collisions would occur with the proper orientation for reaction. 51 Arrhenius Equation Taking the natural logarithm of both sides, the equation becomes y = mx + b When k is determined experimentally at several temperatures, Ea can be calculated from the slope of a plot of ln k vs. 1/T. 52 Reaction Mechanisms The sequence of events that describes the actual process by which reactants become products is called the reaction mechanism. Reactions may occur all at once or through several discrete steps. Each of these processes is known as an elementary reaction or elementary process. 53 Reaction Mechanisms The molecularity of a process tells how many molecules are involved in the process. The rate law for an elementary step is written directly from that step. 54 Multistep Mechanisms In a multistep process, one of the steps will be slower than all others. The overall reaction cannot occur faster than this slowest, rate-determining step. 55 Slow Initial Step NO2 (g) + CO (g) NO (g) + CO2 (g) The rate law for this reaction is found experimentally to be Rate = k [NO2]2 CO is necessary for this reaction to occur, but the rate of the reaction does not depend on its concentration. This suggests the reaction occurs in two steps. 56 Slow Initial Step A proposed mechanism for this reaction is Step 1: NO2 + NO2 NO3 + NO (slow) Step 2: NO3 + CO NO2 + CO2 (fast) The NO3 intermediate is consumed in the second step. As CO is not involved in the slow, rate-determining step, it does not appear in the rate law. 57 Fast Initial Step The rate law for this reaction is found (experimentally) to be Because termolecular (= trimolecular) processes are rare, this rate law suggests a two-step mechanism. 58 Fast Initial Step A proposed mechanism is Step 1 is an equilibrium- it includes the forward and reverse reactions. 59 Fast Initial Step The rate of the overall reaction depends upon the rate of the slow step. The rate law for that step would be But how can we find [NOBr2]? 60 Fast Initial Step NOBr2 can react two ways: With NO to form NOBr By decomposition to reform NO and Br2 The reactants and products of the first step are in equilibrium with each other. Therefore, Ratef = Rater 61 Fast Initial Step Because Ratef = Rater , k1 [NO] [Br2] = k−1 [NOBr2] Solving for [NOBr2] gives us k1 k−1 [NO] [Br2] = [NOBr 2] 62 Fast Initial Step Substituting this expression for [NOBr2] in the rate law for the rate-determining step gives 63 Reaction Energy Diagram for the two-step NO2-F2 reaction 2NO2(g) + F2(g) 2NO2F(g) rate = k[NO2][F2] Two transition states and one intermediate are involved. The first step is rate-determining. The reaction is exothermic (thermodynamics). 64 What happens when a fast reversible step(s) occurs prior to the rate-determining step? 2NO(g) + O2(g) 2NO2 (g) Rate law: rate = k[NO]2[O2] Proposed Mechanism Step 1: NO(g) + O2(g) NO3(g) fast and reversible Step 2: NO3(g) + NO(g) 2NO2(g) slow; rate-determining Rate laws for the two elementary steps: Step 1: rate1 (fwd) = k1[NO][O2]; rate1 (rev) = k-1[NO3] Step 2: rate2 = k2[NO3][NO] Step 2 (rate-determining) contains [NO3] which does not appear in the experimental rate law! 65 If Step 1 is at equilibrium, then.... rate1 (fwd) = rate1 (rev) k1[NO][O2] = k-1[NO3] Solving for [NO3]: [NO3] = (k1/k-1)[NO][O2] Substituting into the rate law for rate-limiting Step 2: rate2 = k2[NO3][NO] = k2 (k1/k-1)[NO][O2][NO] = [(k1k2)/k-1][NO]2[O2] Conclusion: The proposed mechanism is consistent with the kinetic data. 66 Catalysts Catalysts increase the rate of a reaction by decreasing the activation energy of the reaction. Catalysts change the mechanism by which the process occurs. The catalyzed reaction proceeds via a different mechanism than the uncatalyzed reaction. Both forward and reverse reactions are catalyzed; reaction thermodynamics is unaffected! 67 Energy diagram of an uncatalyzed and catalyzed reaction Note that both reactions exhibit the same thermodynamics! The catalyzed and uncatalyzed reactions occur via different pathways. 68 Uncatalyzed reaction: A + B product Catalyzed reaction: A + catalyst C C + B product + catalyst Types of Catalysts  Homogeneous: exists in solution with the reaction mixture  Heterogeneous: catalyst and reaction mixture are in different phases 69 70 Homogeneous Catalysis The Mechanism of Acid-catalyzed Organic Ester Hydrolysis R-COOR’ + H2O + H+ R-COOH + R’OH + H+ ester acid alcohol The reaction rate is slow at neutral pH (pH 7.0), but increases significantly at acidic pH (pH 2). H+ ion catalyzes the reaction at low pH; what is the molecular basis for the catalysis by H+? 71 Heterogeneous Catalysis: Metal-catalyzed hydrogenation of ethylene H2C CH2 (g) + H2 (g) H3C CH3 (g) Ni, Pd or Pt 72 Enzymes Enzymes are catalysts in biological systems. The substrate fits into the active site of the enzyme much like a key fits into a lock. 73 Two Models of Enzyme Action lock and key induced fit 74

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